Statistics of clustering of ultra-high energy cosmic rays and the number of their sources

Abstract

Observation of clustering of ultra-high energy cosmic rays (UHECR) suggests that they are emitted by compact sources. Assuming small deflection of UHECR during the propagation, the statistical analysis of clustering allows to estimate the spatial density of the sources, h, including those which have not yet been observed directly. When applied to astrophysical models involving extra-galactic sources, the estimate based on 14 events with energy E>10^{20} eV gives h ~ 6 X 10^{-3} Mps^{-3}. With increasing statistics, this estimate may lead to exclusion of the models which associate the production of UHECR with exceptional galaxies such as AGN, powerful radio-galaxies, dead quasars, and models based on gamma ray bursts.